This invention relates to an optical fiber grating defined on an optical fiber.
There is a demand for optical fiber gratings that can be designed and manufactured such that their response is tailored to ideal responses.
In many applications such as dense wavelength division multiplexing (WDM) transmission systems and satellite communications, optical amplifiers and transmitters, optical filters having ideal amplitude and phase responses are desired in order to maximize bandwidth or to optimize the filtering function provided by the fiber Bragg grating.
Conventional fiber Bragg gratings are designed using Fourier Transform methods to determine line spacing and the like, and are manufactured using an ultra violet laser and a phase mask in order to etch lines onto an optical fiber. The resulting series of lines creates a filter that in many instances has a frequency response that is not closely matched to the optimal frequency response for the application.
High-speed, high-capacity optical fiber communication systems depend critically on the availability of high performance optical filters to accomplish a number of functions such as selection of closely packed wavelength-division-multiplexed channels or efficient compensation of link dispersion. To this end, there is a strong demand for grating-based optical devices that can be designed and manufactured such that their response is tailored as close to ideal response as possible. The technology of UV-written fiber gratings has reached now the necessary maturity to implement these high performance filters. There are a number of methods and different approaches in designing high quality grating devices. Among them, Fourier-Transform based and Electromagnetic Inverse Scattering (IS) techniques are known to offer a great variety of possibilities for the design of gratings with various degrees of accuracy.
The simplest grating design approach exploits the approximate Fourier transform (FT) relation that exists between the filter spectral response and the grating coupling function. This is a single-step process and provides the entire coupling constant distribution along the grating length. This method, also know as the first-order Born approximation, takes into account only a single first-order reflection from each line of the grating medium. The method ignores the higher order contributions stemming from multiple reflections between different lines of the grating medium and it is, therefore, applicable only to the design of low reflectivity gratings. Several modifications of the method have been proposed that improved its performance and extended its applicability to relatively high reflectivities, enabling the design of practical fiber grating filters. However, this synthesis approach is approximate in nature and, consequently, not reliable for the design of very complex and strong filters where all the higher-order multiple reflections are important and should be taken into account.
Another group of grating design algorithms is based on Inverse Scattering (IS) techniques, expressed in terms of integral equations. These types of solutions were first developed in the context of the inversion of the unidimensional Schrodinger equation, and then applied to the problem of two-component scattering. The IS integral equations are usually derived using general arguments resulting from the causality of the propagation of signals. They invert the desired grating response in the spatial frequency domain and express the grating complex coupling-constant distribution as a superposition of generalized high-order spatial harmonics. Therefore, the IS methods based on integral equations can be regarded as generalized Fourier Transform Methods.
The main drawback of integral IS methods is the difficulty involved in solving the integral equations. However, analytical IS integral-equation exact solutions can be found in the literature, when the required filter spectral response is expressed in terms of rational functions. It should be stressed that such an approach provides an exact solution to the approximated problem (approximations are inevitably introduced when expressing the required filter spectral response in terms of rational functions). This again is a one-step design process. This method has been applied in designing practical corrugated filters. However, the need to approximate the desired spectral response by rational functions is cumbersome and has resulted in compromised performance.
To overcome this limitation, an iterative solution of the IS integral equations was proposed to synthesize arbitrary spectral responses. It should be stressed that this is a parallel iteration process inverting the grating response in the spatial-frequency domain. The initial step is identical to the first-Born approximation, which, as we have already mentioned, corresponds to a simple inverse Fourier transform. Each subsequent iteration step effectively adds generalized higher-order spatial harmonics over the entire reconstructed grating profile. Therefore, each iteration alters the coupling strength along the entire grating length or, equivalently, every grating point is affected by each iteration step. Several fiber-grating devices, designed with this iterative method, have already been fabricated proving the usefulness of the method. However, the iterative solution of the IS integral equations has two main weaknesses. Firstly, the solution is approximate due to the finite number of iterations involved, which means that only a limited number of reflections within the medium are considered. This is particularly noticeable for strong gratings with discontinuities in the coupling strength. The second drawback is the low algorithm efficiency, with a complexity that grows as O(N3), where N is the number of points in the grating. Both of these weaknesses can be overcome, as the matrix coefficients that appear in the integral equation permit the use of fast algorithms of O(N2) for its solution. Several other, in essence similar, iterative inverse scattering approaches have been described in the literature.
Finally, there exists a third group of exact IS algorithms called differential or direct methods. These techniques, developed first in the context of geophysics, exploit fully the physical properties of the layered-medium structure in which the waves propagate. The methods are based again on causality arguments, and identify the medium recursively layer by layer. For this reason they are sometimes called layer-peeling or dynamic deconvolution algorithms. The complexity of the algorithm grows only as O(N2) and is usually well suited for parallel computation.
It is therefore an aim of the present invention to provide a fiber Bragg grating that matches the ideal response and to provide a method for manufacturing fiber Bragg gratings that result in filters with a substantially ideal response.
According to a non-limiting embodiment of the present invention, there is provided an optical waveguide having an optical fiber on which is defined a Bragg grating. The Bragg grating is designed using a serial iterative process. More particularly, the Bragg grating comprises a plurality of lines etched into the optical fiber, each line defining a strength, and each line have a line spacing between itself and adjacent lines in the grating. The iterative process for calculating subsequent line spacing for the grating can be a function of the strength and line spacing of the previous segments of the grating, and the impulse response thereof. The strength and line spacing define a coupling function.
By associating a length z0 to the subgrating, and a corresponding time t0 for light traveling at a group velocity within the grating subgrating to travel the length of the subgrating and reflect back the to beginning of the subgrating, a length increment xcex4z with a corresponding time increment xcex4t can be selected. The coupling function at the length z0 is substantially equal to the selected impulse response at the time t0 minus the impulse response of the grating from the first end of the grating to the length z0. The coupling function at the length z0 plus xcex4z is substantially equal to minus two times the difference between the selected impulse response hR at the time t0 plus xcex4t and a second impulse response hT at the time t0 plus xcex4t.
The Bragg grating can further be characterized by a series of diminishing reflective signals. The serial iterative process can comprises applying a time window function having an overall width T, and a time delay, and the window function can be shifted by the time delay to limit the number of reflective signals considered in the iterative process. The time window function is chosen to contain a substantial amount of the selected impulse response hR. For example, the time window function and can contain 99.9%, 99%, or 95% of the selected impulse response hR.
The Bragg grating can further be characterized by a desired impulse response hR. In the iterative process the desired impulse response hR can be multiplied by the time window function to determine the distance between a first line of the Bragg grating and a second line of the Bragg grating.
In one embodiment of the invention the Bragg grating characterizes a selected grating wavelength response, and the selected grating wavelength response is selected from the group consisting of a substantially square dispersionless filter, a substantially square dispersion compensator, a substantially square second-order dispersion compensator, a substantially square third-order dispersion compensator, a filter having multiple wavelength peaks, a filter having multiple wavelength peaks that are substantially square, and a filter having multiple wavelength peaks that are substantially square and have substantially the same peak reflectivity. The selected grating wavelength response can also be a filter having multiple wavelength peaks that are substantially square and are defined by a peak reflectivity, where the multiple wavelength peaks have substantially the same peak reflectivity and further have a reduced peak coupling ratio requirement.
The invention further includes an optical fiber filter, the filter comprising a Bragg grating defined by a grating response and an impulse response. The filter is defined by a filter response which is a predetermined function of the grating response, and the grating response is selected to be a function of the impulse response at a time t0 and at a length z0 along the Bragg grating.
In one embodiment, the invention provides for an optical waveguide defining a Bragg grating having a first end and a second end. Light propagating in the optical waveguide is defined by a group velocity. The Bragg grating is defined by a selected grating reflectivity and dispersion response which varies with a wavelength. The grating is also defined by a selected impulse response hR that varies with a time t, and a coupling function that varies with a length z that is measured from the first end of the grating. A first length z0, with a corresponding first time t0, that extends from the first end to the first length z0 defines a subgrating in the overall grating. A length increment xcex4z with a corresponding time increment xcex4t defines the line spacing for the next line of the grating following the subgrating. The subgrating has a second impulse response hT that varies with a time t. The first length z0 is equal to the first time t0 multiplied by the group velocity divided by 2, and the length increment xcex4z is equal to the time increment xcex4t multiplied by the group velocity divided by 2. The selected impulse response and the selected grating reflectivity and dispersion response are Fourier Transform pairs. The coupling function at the length z0 plus xcex4z is substantially equal to minus two times the difference between the selected impulse response hR at the time t0 plus xcex4t and the second impulse response hT at the time t0 plus xcex4t. The Bragg grating is designed such that z0 can be successively, iteratively stepped from the first end to the second end resulting in an actual impulse response that is substantially equal to the selected impulse response.
The invention also provides a method for designing and manufacturing an optical fiber Bragg grating having a selected grating response. The method includes the steps of providing an optical fiber, defining a starting point for the Bragg grating to be fabricated on the optical fiber, and etching a first line on the optical fiber. Then a subgrating length is defined on the optical fiber by moving a distance z0 along the optical fiber. A second line is then etched on the optical fiber at the distance z0. A response for the subgrating is calculated, and the response for the subgrating is used to determine the line spacing for the next line in the grating.